When an isotropic antenna transmits power it does so in all directions. At some distance R all that power is passing thru the surface of an imaginary sphere of radius R. At distance 2R, the same amount of power is passing thru the surface of a sphere of twice the radius etc etc..
An isotropic receive antenna placed at some distance to the transmit antenna can only collect a small fraction of that power. It has, what is called, an effective area (or antenna aperture) and this is measured in sq metres.
This means that two isotropic antennas (that don't overlap) can each collect their own power and the transmit antenna doesn't know - it believes (if it had the power to reason) that all the power transmitted is going to reach the far ends of the universe.
The same is basically true of any antenna - providing the effective apertures don't overlap they'll each collect the "theoretical" power transmitted by that sort of antenna.
All this falls down when you get to the near field because in the near field you can effect the transmit antenna by loading.
Think of it like a light-bulb - several people in the room can each see the light but if one person stands in front of another then somebody misses out.
Of course it is possible in theory. But very very inefficient in practice.
Inductance of the primary coil (e.g.; A=10000mm\$^2\$ cross sectional area, \$\ell\$=100mm length, 10,000 turns) is
$$ L = \dfrac{\mu A N^2}{\ell} = \dfrac{(4\pi 10^{-7} \text{H/m}) (0.01\text{m}^2) (10000)^2}{0.1\text{m}} = 4\pi \text{H} = 12.5664\text{H}. $$
Resistance of the primary winding is
$$ R_p = \dfrac{2\pi\sqrt{\dfrac{A}{\pi}}N\rho_{cu}}{a} = \dfrac{2 \pi \sqrt{\dfrac{0.01\text{m}^2}{\pi}} (10000) (16.78 \times 10^{-9} \Omega\text{m})}{10^{-6}\text{m}^2} = 59.48 \Omega. $$
The RMS magnetizing current which will be wasted on the primary side will then be (ignoring the resistance of the wire)
$$ I_m = \dfrac{V_p}{Z_p} = \dfrac{V_p}{\sqrt{X_p^2 + R_p^2}} = \dfrac{V_p}{\sqrt{(2\pi f L)^2 + (59.48\Omega)^2}} = \dfrac{220\text{V}}{\sqrt{(2\pi (50\text{Hz}) (12.5664\text{H}))^2 + (59.48\Omega)^2}} = \dfrac{220\text{V}}{\sqrt{(3947.85\Omega)^2 + (59.48\Omega)^2}} = \dfrac{220\text{V}}{3948.30\Omega} = 55.72\text{mA} $$
which is low enough for most use cases.
Assume that you use copper wire of cross sectional area a=1mm\$^2\$ and the density of copper is d=8.96 g/cm\$^3\$. The mass of copper you need is (assuming that it fits in the given space)
$$ \text{m} = 2\pi\sqrt{\dfrac{A}{\pi}}aNd = 2 \pi \sqrt{\dfrac{0.01\text{m}^2}{\pi}}(10^{-6}\text{m}^2) (10000) (8960 \text{kg}/\text{m}^3) = 63.52 \text{kg}. $$
Note that, the same amount of copper you need on the secondary side if you want to get the same voltage level. If we take price of copper as p=6$/kg, total price of copper used will be $762.24.
Real power loss due to magnetizing current will be
$$ P_{\text{loss},m} = I_m^2R_p = (0.05572\text{A})^2(59.48\Omega) = 185 \text{mW}. $$
Real power loss when transferring 10A current will be
$$ P_{\text{loss},10A} = (10\text{A})^2(59.48\Omega) = 5.948 \text{kW}, $$
which means there won't be 220V on the secondary side due to heavy voltage drop on the primary side winding resistance. You need much bigger wire radius, more copper, more money!
You may do some optimization. For example, you may reduce number of turns, which will increase magnetizing current and reduce copper losses. But even at the optimum point, it will still be very inefficient.
Because of this, people don't transfer large power though air and they use cores for it.
Best Answer
Polarity will not work; this sort of "wireless power transmission" is really a transformer, and transformers only pass AC.
You could potentially use the orientation of the field, ie, have two solutions at right angles to each other, but a lot of contemporary solutions have the field oriented vertically, so that won't work either.
Instead, what you'd probably want to do is to modulate information in a detail of the drive signal - possibly something as simple as a small change in frequency, or a pattern of pulses and gaps.
Or you could just use some cheap radio technology.
The advantage of the latter is that you could give in and use a battery for power after all, which you're likely to find quite a bit easier to get working.
Easiest still would be a battery and some reed switches, and then put magnets or electromagnets in the base; then you don't even need to do low-power design to preserve your battery, since the reed switch functions as an actual switch.